While planar shock waves are known to be stable to small perturbations in the sense that the perturbation amplitude decays over time, it has also been suggested that plane propagating shocks can develop singularities in some derivative of their geometry (Whitham (1974) Linear and nonlinear waves. Wiley, New York) in a nonlinear, wave reinforcement process. We present a spectral-based analysis of the equations of geometrical shock dynamics that predicts the time to singularity formation in the profile of an initially perturbed planar shock for general shock Mach number. We find that following an initially sinusoidal perturbation, the shock shape remains analytic only up to a finite, critical time that is a monotonically decreasing function of the initial perturbation amplitude. At the critical time, the shock profile ceases to be analytic, corresponding physically to the incipient formation of a “shock-shock” or triple point. We present results for gas-dynamic shocks and discuss the potential for extension to shock dynamics of fast MHD shocks.

Meeting Name

31st International Symposium on Shock Waves, ISSW31 (2017: Jul. 9-14, Nagoya, Japan)


Mechanical and Aerospace Engineering


This research was supported by the KAUST Office of Sponsored Research under award URF/1/2162-01.

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 2017 International Shock Wave Institute (ISWI), All rights reserved.

Publication Date

14 Jul 2017